Article

Free access

Parallelization, amplification, and exponential time simulation of quantum interactive proof systems

Authors:

Alexei Kitaev,

John WatrousAuthors Info & Claims

STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computing

Pages 608 - 617

https://doi.org/10.1145/335305.335387

Published: 01 May 2000 Publication History

PDF eReader

References

[1]

D. Aharonov, A. Kitaev, and N. Nisan. Quantum circuits with mixed states. In Proceedings of the Thirtieth Annual A CM Symposium on Theory of Computing, pages 20-30, 1998.

Digital Library

Google Scholar

[2]

F. Alizadeh. Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM Journal on Optimization, 5(1):13-51, 1995.

Digital Library

Google Scholar

[3]

L. Babai. Trading group theory for randomness. In Proceedings of the Seventeenth Annual A CM Symposium on Theory of Computing, pages 421-429, 1985.

Digital Library

Google Scholar

[4]

L. Babai, L. Fortnow, and C. Lund. Non-deterministic exponential time has two-prover interactive protocols. Computational Complexity, 1(1):3-40, 1991.

Crossref

Google Scholar

[5]

A. Barenco. A universal two-bit gate for quantum computation. Proceedings of the Royal Society of London, 449:679-683, 1995.

Crossref

Google Scholar

[6]

A. Barenco, C. H. Bennett, R. Cleve, D. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter. Elementary gates for quantum computation. Physical Review Letters A, 52:3457-3467, 1995.

Crossref

Google Scholar

[7]

E. Bernstein and U. Vazirani. Quantum complexity theory. SIAM Journal on Computing, 26(5):1411-1473, 1997.

Digital Library

Google Scholar

[8]

A. Berthiaume. Quantum computation. In L. Hemaspaandra and A. Selman, editors, Complexity Theory Retrospective II, pages 23-50. Springer, 1997.

Digital Library

Google Scholar

[9]

J. Cai, A. Condon, and R. Lipton. On bounded round multi-prover interactive proof systems. In Proceedings of the Fifth Annual Conference on Structure in Complexity Theory, pages 45-54, 1990.

Crossref

Google Scholar

[10]

D. Deutsch. Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London, A400:97-117, 1985.

Crossref

Google Scholar

[11]

D. Deutsch. Quantum computational networks. Proceedings of the Royal Society of London, A425:73-90, 1989.

Crossref

Google Scholar

[12]

D. DiVincenzo. Two-bit gates are universal for quantum computation. Physical Review A, 50:1015-1022, 1995.

Crossref

Google Scholar

[13]

U. Feige. On the success probability of two provers in one-round proof systems. In Proceedings of the Sixth Annual Conference on Structure in Complexity Theory, pages 116-123, 1991.

Crossref

Google Scholar

[14]

U. Feige and L. Lovfisz. Two-prover one-round proof systems: their power and their problems. In Proceedings of the Twenty-Fourth Annual A CM Symposium on Theory of Computing, pages 733-744, 1992.

Digital Library

Google Scholar

[15]

C. Fuchs and J. van de Graaf. Cryptographic distinguishability measures for quantum-mechanical states. IEEE Transactions on Information Theory, 45(4):1216-1227, 1999.

Digital Library

Google Scholar

[16]

O. Goldreich. A taxonomy of proof systems. In L. Hemaspaandra and A. Selman, editors, Complexity Theory Retrospective II, pages 109-134. Springer- Verlag, 1997.

Digital Library

Google Scholar

[17]

S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM Journal on Computing, 18(1):186-208, 1989. Preliminary version appeared in Proceedings of the Eighteenth Annual A CM Symposium on Theory of Computing, pages 291-304, 1985.

Digital Library

Google Scholar

[18]

S. Goldwasser and M. Sipser. Private coins versus public coins in interactive proof systems. In S. Micali, editor, Randomness and Computation, volume 5 of Advances in Computing Research, pages 73-90. JAI Press, 1989.

Google Scholar

[19]

M. GrStschel, L. Lov~sz, and A. Schrijver. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica, 1, 1981.

Google Scholar

[20]

R. Horn and C. Johnson. Matrix Analysis. Cambridge University Press, 1985.

Digital Library

Google Scholar

[21]

L. Hughston, R. Jozsa, and W. Wootters. A complete classification of quantum ensembles having a given density matrix. Physics Letters A, 183:14-18, 1993.

Crossref

Google Scholar

[22]

R. Jozsa. Fidelity for mixed quantum states. Journal of Modern Optics, 41(12):2315-2323, 1994.

Crossref

Google Scholar

[23]

A. Kitaev. Quantum computations: algorithms and error correction. Russian Mathematical Surveys, 52(6):1191-1249, 1997.

Crossref

Google Scholar

[24]

D. Lapidot and A. Shamir. Fully parallelized multi prover protocols for NEXP-time. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 13-18, 1991.

Digital Library

Google Scholar

[25]

C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic methods for interactive proof systems. Journal of the A CM, 39(4):859-868, 1992.

Digital Library

Google Scholar

[26]

A. Shamir. IP = PSPACE. Journal of the A CM, 39(4):869-877, 1992.

Digital Library

Google Scholar

[27]

P. Shor. Fault-tolerant quantum computation. In Pro. ceedings of the 37th Annual Symposium on Foundations of Computer Science, pages 56-65, 1996.

Digital Library

Google Scholar

[28]

P. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5):1484-1509, 1997.

Digital Library

Google Scholar

[29]

L. Vandenberghe and S. Boyd. Semidefinite programruing. SIAM Review, 38(1):49-95, 1996.

Digital Library

Google Scholar

[30]

J. Watrous. PSPACE has constant-round quantum interactive proof systems. In Proceedings of the dOth Annual Symposium on Foundations of Computer Science, pages 112-119, 1999.

Digital Library

Google Scholar

[31]

A. Yao. Quantum circuit complexity. In Proceedings of the 3jth Annual Symposium on Foundations of Computer Science, pages 352-361, 1993.

Google Scholar

Cited By

View all

Bostanci JQian LSpooner NYuen HMohar BShinkar IO'Donnell R(2024)An Efficient Quantum Parallel Repetition Theorem and ApplicationsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649603(1478-1487)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649603
Nema ASen P(2024)High Probability Decoupling via Approximate Unitary Designs and Efficient Relative ThermalizationIEEE Transactions on Information Theory10.1109/TIT.2024.335906570:4(2590-2616)Online publication date: Apr-2024
https://doi.org/10.1109/TIT.2024.3359065
Ikeda KLowe A(2024)Quantum interactive proofs using quantum energy teleportationQuantum Information Processing10.1007/s11128-024-04448-023:6Online publication date: 12-Jun-2024
https://doi.org/10.1007/s11128-024-04448-0
Show More Cited By

Index Terms

Parallelization, amplification, and exponential time simulation of quantum interactive proof systems

Recommendations

Quantum discord amplification of fermionic systems in an accelerated frame

Quantum discord of fermionic systems in the relativistic regime, that is, beyond the single-mode approximation (SMA) is investigated. It is shown that quantum discord is amplified for the fermionic system in non-inertial frames irrespective of the ...
Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states: Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states

Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span nonlocal state or sequential application of few-qubit entangling gates are needed to produce ...
Digital quantum simulation with Rydberg atoms

We discuss in detail the implementation of an open-system quantum simulator with Rydberg states of neutral atoms held in an optical lattice. Our scheme allows one to realize both coherent as well as dissipative dynamics of complex spin models involving ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computing

May 2000

756 pages

ISBN:1581131844

DOI:10.1145/335305

Chairmen:
Frances Yao,
Eugene Luks

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 2000

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

STOC00

Sponsor:

SIGACT

STOC00: The 32nd Annual ACM Symposium on Theory of Computing

May 21 - 23, 2000

Oregon, Portland, USA

Acceptance Rates

STOC '00 Paper Acceptance Rate 85 of 182 submissions, 47%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Upcoming Conference

STOC '25

Sponsor:
sigact

57th Annual ACM Symposium on Theory of Computing (STOC 2025)

June 23 - 27, 2025

Prague , Czech Republic

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

82
Total Citations
View Citations
1,143
Total Downloads

Downloads (Last 12 months)208
Downloads (Last 6 weeks)42

Reflects downloads up to 09 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Bostanci JQian LSpooner NYuen HMohar BShinkar IO'Donnell R(2024)An Efficient Quantum Parallel Repetition Theorem and ApplicationsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649603(1478-1487)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649603
Nema ASen P(2024)High Probability Decoupling via Approximate Unitary Designs and Efficient Relative ThermalizationIEEE Transactions on Information Theory10.1109/TIT.2024.335906570:4(2590-2616)Online publication date: Apr-2024
https://doi.org/10.1109/TIT.2024.3359065
Ikeda KLowe A(2024)Quantum interactive proofs using quantum energy teleportationQuantum Information Processing10.1007/s11128-024-04448-023:6Online publication date: 12-Jun-2024
https://doi.org/10.1007/s11128-024-04448-0
Metger TYuen H(2023)stateQIP = statePSPACE2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00082(1349-1356)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00082
Deng ZWang XDong B(2023)Quantum computing for future real-time building HVAC controlsApplied Energy10.1016/j.apenergy.2022.120621334(120621)Online publication date: Mar-2023
https://doi.org/10.1016/j.apenergy.2022.120621
Yan J(2023)General Properties of Quantum Bit Commitments (Extended Abstract)Advances in Cryptology – ASIACRYPT 202210.1007/978-3-031-22972-5_22(628-657)Online publication date: 25-Jan-2023
https://doi.org/10.1007/978-3-031-22972-5_22
Broadbent AGrilo A(2022)QMA-Hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-KnowledgeSIAM Journal on Computing10.1137/21M140729X51:4(1400-1450)Online publication date: 31-Aug-2022
https://doi.org/10.1137/21M140729X
Kahanamoku-Meyer GChoi SVazirani UYao N(2022)Classically verifiable quantum advantage from a computational Bell testNature Physics10.1038/s41567-022-01643-718:8(918-924)Online publication date: 1-Aug-2022
https://doi.org/10.1038/s41567-022-01643-7
Ghosh SWatrous J(2022)Complexity Limitations on One-turn Quantum Refereed GamesTheory of Computing Systems10.1007/s00224-022-10105-967:2(383-412)Online publication date: 10-Dec-2022
https://doi.org/10.1007/s00224-022-10105-9
Gharibian SSantha MSikora JSundaram AYirka J(2022)Quantum generalizations of the polynomial hierarchy with applications to QMA(2)Computational Complexity10.1007/s00037-022-00231-831:2Online publication date: 20-Sep-2022
https://dl.acm.org/doi/10.1007/s00037-022-00231-8
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Quantum discord amplification of fermionic systems in an accelerated frame

Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states: Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states

Digital quantum simulation with Rydberg atoms